Estimating the price incentive

304 F. Kuchler, S. Hamm Agricultural Economics 22 2000 299–308 ers are unlikely to have discovered a practical means for breeding for susceptibility and kept the discovery secret from the scientific community. Thus, indem- nity price increases should have reduced or left un- changed the susceptible subpopulation. Physical characteristics of the problem and the im- pact of prices on the effectiveness with which infected animals are identified determine whether an eradica- tion program will quickly succeed or never make a de- tectable impact on the problem. Technology was not advanced enough for the scrapie eradication program to search for susceptible animals. Instead, the program offered a bounty for confirmed cases, a subset of the susceptible animals.

4. Estimating the price incentive

Several analysts have speculated that prices in- fluenced scrapie reporting. Wineland et al. 1998 included a graphic overlaying confirmed cases on the nominal indemnity payment, suggesting a connection between indemnity payment levels and the num- ber of reports. USDA, APHIS, VS, 1991 was more explicit: “The reporting of scrapie has been notably influ- enced by the real inflation-adjusted value of the indemnity payment. p. 3” However, the agency report did not suggest the hy- pothesis has been tested empirically. Similar speculation accompanied both the British and Portuguese indemnity programs to control BSE. Several public health officials argued that prices de- termine whether programs are successful in removing diseased animals from the food supply. Summarizing remarks of Dr. Richard Lacey, Reuters reported “. . . farmers are under enormous pressure not to report cases of BSE because the UK government has cut compensation levels for sick animals Reaney, 1998.” The Wall Street Journal summarized remarks of Ramiro Doutel Mascarenhas, vice director of the vet- erinary section of the Ministry of Agriculture in Lis- bon: “. . . farmers who report diseased animals are paid more than they are worth, so there is no financial incentive to send a sick animal to the slaughterhouse Stecklow, 1998.” Fig. 1 shows the time pattern of reported cases since from the beginning of the eradication program in 1952 through its end in 1992, along with succeeding years covered by the voluntary certification program. Clearly, neither program eradicated the disease. But even if the eradication program had been partially suc- cessful, infected sheep would be increasingly difficult to find. In that case, the incentive to find additional animals created by rising indemnity payment levels would decline. That is, the supply of infected sheep would become increasingly price inelastic. Here, we show that the supply of scrapie-infected sheep was price elastic and that the level at which the indemnity payment was set offered a strong behavioral incentive. We let the quantity of confirmed scrapie cases, the supply of infected sheep offered to the Federal govern- ment, depend on the relative prices farmers anticipate P e t A desired supply is thus a function of expected prices Eq. 6. Q ∗ t = β + β 1 P e t + ε t 6 Neither variable is directly observable. Like all other agricultural commodities, it takes time to produce sheep, whether healthy or ill. Thus, com- plete responses to relative prices may not occur imme- diately. Instead, the supply of scrapie-infected sheep may adjust partially each period Eq. 7. 1Q t = λQ ∗ t − Q t − 1 + η t 7 The error terms ε t and η t are assumed to be normal, independently and identically distributed random vari- ables with mean zero and constant variance. Substi- tuting Eq. 7 into Eq. 6 eliminates Q, one of the unobservable variables Eq. 8. Q t = λβ + λβ 1 P e t + 1 − λQ t − 1 + v t where v t = λε t + η t 8 A ewe is a capital asset and farmers continually face the choice of whether to continue using the ewe to pro- duce slaughter lambs or to sell the asset at its market value. The scrapie indemnity program offered farm- ers an additional option for their infected sheep. They could sell to the Federal government. Here, we focus on the choice between accepting the asset’s salvage value and selling to the Federal government and the future productivity of maintaining an animal in the breeding stock. F. Kuchler, S. Hamm Agricultural Economics 22 2000 299–308 305 Assuming the ewe market is efficient, we know the price should be equivalent to the present value of the expected profits from slaughter lambs. That is, if we had a consistent series of market prices for breeding stock, we should find little difference from the present value of expected profits from slaughter lambs. Em- pirically, the two series would move together if we could measure them both. However, no consistent data on ewe prices exist as these are quite heterogeneous assets, with values likely varying among breeds. We use the current price of slaughter lambs as a proxy for the value of a ewe. Unlike the slaughter lamb price, the indemnity payment was set by fiat and thus need not bear any relation to market prices. We model the major measur- able choices that faced sheep farmers with potentially scrapie-infected sheep. Our working hypothesis is that it was not immediately obvious that all infected sheep were in fact infected. That is, some infected sheep may have been sold for slaughter. The major alternative use of a scrapie-infected sheep was to acknowledge the illness and receive the indemnity payment. Thus, we model expected relative prices: the maximum in- demnity payment relative to the price of slaughter lambs. We define the relative prices farmers faced as: P t = Maximum indemnity payment in period t Market price of slaughter lambs in period t 9 When indemnity payments increased relative to the slaughter lamb price representing the value of a ewe in production rise, farmers may have looked harder for infected animals. Similarly, when indemnity pay- ments were reduced relative to slaughter lamb prices, the incentive to find infected animals was reduced. In that case, fewer confirmations of scrapie would be anticipated. Because indemnity payments changed following Federal government fiscal years, we constructed all variables on a fiscal year basis. Variables were trans- formed to natural logarithms so parameter estimates could be interpreted as elasticities. The dependent variable is a log transformed count of the num- ber of confirmed scrapie cases in the United States each fiscal year. APHIS maintained records of each confirmed scrapie case. From confirmation dates, we constructed fiscal year totals. We calculated an annual slaughter lamb price also on a fiscal year basis and constructed the relative price series. Slaughter lamb prices received by farm- ers are from the National Agricultural Statistics Ser- vice annual price survey reports US Department of Agriculture, National Agricultural Statistics Service, Agricultural Statistics Board. We cannot observe expected prices, only realized prices. We assumed that farmers extrapolated from past prices when forecasting prices and could observe cyclical movements in prices. Thus, we let log trans- formed relative prices follow an extrapolative model. Identifying the ARIMA model that the relative price series followed strongly suggested a random walk. Autocorrelations of the relative price series declined slowly and the partial autocorrelations spiked at lag 1 and nowhere else. After differencing, no significant autocorrelations or partial autocorrelation were signif- icantly different from zero. Dickey–Fuller tests con- firmed the need to difference once. None of the three Dickey–Fuller test statistics approached critical val- ues for the undifferenced data. After differencing, all three exceeded 1 critical values, strongly suggest- ing stationarity of the differenced series. Augmented Dickey–Fuller tests showed exactly the same results as lagged dependent variables were uniformly insignifi- cant. Thus, our model for expected prices is Eq. 10. P e t = P t − 1 10 During two periods 1957–1964 and 1976–1982, participating in the program had some negative con- sequences. If a farmer sold one or more confirmed scrapie-infected sheep to the government, the govern- ment would depopulate the flocks containing those sheep. Also, if the sheep had been purchased, the flock from which the infected sheep had come were depop- ulated. We assume these consequences would have had a chilling influence on future transactions among farmers and would have made a farmer less likely to participate in the program. In other years, flock depop- ulation was not emphasized bloodlinesurveillance program. For convenience, we refer to the years in which the bloodlinesurveillance program was in ef- fect as the unrestricted period. Consistent with our price variable, we defined the dummy variable equal to 1 for the years in which these negative consequences were not enforced in the previous year unrestricted period and 0 for all other years restricted period. 306 F. Kuchler, S. Hamm Agricultural Economics 22 2000 299–308 Table 1 Supply function parameter estimates Estimates t-statistics λ 0.5170 4.9305 β −1.7429 −2.5963 γ 2.9915 5.7637 γ 1 0.4004 1.8791 Table 2 Estimated price elasticities of supply Short-run Long-run Less restrictive period 1.7536 2.9915 More restrictive period 1.5466 3.3919 The estimated model contained a constant, the ex- pected relative prices, a dummy variable shifting the price slope β 1 =γ +γ 1 D t and a partial adjustment parameter. ln Q t = λβ + λγ + γ 1 D t ln P t − 1 +1 − λ ln Q t − 1 + e t 11 Eq. 11 was estimated with non-linear least squares, yielding parameter estimates and asymptotic t-statistics Table 1. Estimating in double-log form yields the short-run one-period price elasticities. During the unrestricted period price elasticity equals λ γ +γ 1 and price elasticity equals λγ when the indemnity payment carried severe penalties. The long-run price elasticity during the unrestricted period is lim λ→ 1 λγ + γ 1 = γ + γ 1 and at the restricted period lim λ→ 1 λγ = γ Estimates of the four price elasticities are reported in Table 2. The diagnostic statistics Table 3 show the model performs well. The Jarque–Bera test indicates no rea- son to reject the null hypothesis that the residuals are independent and normally distributed. We tested for Table 3 Supply function diagnostic statistics Tests Ramsey’s RESET Breusch–Godfrey serial correlation LM test Jarque–Bera residual test Additional variables in logs F p value H χ 2 p value χ 2 p value ˆ Q 2 t and ˆ Q 3 t 0.4934 0.6149 ρ 1 =0 0.0200 0.8875 1.7950 0.4076 ˆ Q 2 t , ˆ Q 3 t , and ˆ Q 4 t 0.3243 0.8078 ρ 1 =ρ 2 =0 0.4475 0.7995 model misspecification following Ramsey’s RESET procedure. To run the test, we followed recommenda- tions of Ramanathan 1995, p. 290, adding fitted val- ues of the dependent variable up to fourth power to Eq. 11. We also tested a lower order for powers of fitted values. Neither test indicates any evidence of misspec- ification. Serial correlation in the error terms would be problematic as the model incorporates a lagged de- pendent variable. The Legrange multiplier LM tests for serial correlation suggest the residuals are white noise. Thus, there is no reason to suspect bias in the parameter estimates. The adjustment coefficient λ=0.5170 indicates that just over half of the gap between realized and de- sired supply closed in 1 year. The speed of adjustment λ −1 =1.9342 indicates full adjustment occurred in just under 2 years. The short-run price elasticity λγ was 1.75 during the less restrictive periods, indicating that a 1 rise in the indemnity payment, relative to the market price of slaughter lambs, yielded a 1.75 increase in the num- ber of confirmed scrapie cases Table 2. Similarly, a 1 increase in the price of slaughter lambs relative to the indemnity payment, yielded a 1.75 reduction in confirmed cases. In the more restrictive period, the price response was slightly less, but still elastic. The long-run impact of a one-period price shock was ap- proximately twice the short-run impact. A 1 price shock was associated with a 3.39 change in the num- ber of confirmed cases, over a nearly 2-year period in the less restrictive years. By itself, Fig. 1 might suggest that over the long run, the number of cases was rising. However, the model explains 81 of the variation in the log-transformed number of cases and, as Table 3 suggests, the residu- als appear to be white noise. That is, the increase ap- pears to be largely due to changing relative prices and program characteristics. F. Kuchler, S. Hamm Agricultural Economics 22 2000 299–308 307 These results are not surprising when viewed in terms of relative prices. The indemnity payment rela- tive to the price of slaughter lamb followed a down- ward trend over the 1962–1977 period. The number of confirmed cases also trends downward over that pe- riod. Following the 333 increase in the indemnity payment in 1978, the number of confirmed cases be- gan trending upward for more than a decade.

5. Conclusions